J. Pkys. Ckem. 1985,89, 5206-5212
5206
The Ag, and Au2 calculations exhibit consistent behavior with respect to the various basis sets and the levels of calculations (SCF, MCSCF, and CI). For Re, neither molecule shows a significant decrease in proceeding from S C F to CI( 1 ) nor upon the addition of the Langhoff-Davidson correction to the CI(2) calculations. In the CI(2) calculations Ag, shows a slightly greater shortening than Au, (0.03 A). Computed bond lengths are dependent on the size of the basis set, the presence of f-type basis functions, the extent of CI performed, and the form of the EP. Differences between the present calculated values and experiment are consistent with other recent molecular calculations involving heavy atoms. This is interpreted as being due more to basis set and electron correlation factors and less to the quality of the REP'S. In particular, for group 11 systems, it may also be necessary to include triple and higher excitations involving the d-shell electrons. However, the inclusion of core polarization and core-valence correlation effects into the REP'S should be examined. Alternatively, fewer electrons may be included in the core, thus permitting the explicit treatment of intershell correlation p h e r ~ o m e n a .This ~ ~ ~results, ~~ however, in considerably more complex calculations due to the increase in the number of electrons that must be treated explicitly.
Deviations between calculated and experimental values of Re are 0.29 8, for Ag, and 0.18 8, for Au2, based on the 1 1-electron CI( 1) results. The additional 0.1 1-8, deviation in Ag, may be due to an uncertainty in the reported experimental value, since it was not obtained by direct measurement. The possibility of uncertainty is further supported by comparing the bond lengths of AgH, AuH, AgAI, and A u A I . ~ The ~ experimental values in the silver compounds are 0.1 1 h 0.03 8, longer than those in the respective gold compounds. The experimental Re values for Ag, and Au2 are the same, 2.47 8,. In addition, it is not unreasonable to expect Re of Au, to experience greater relativistic shortening than Ag2 since such effects are substantially greater in gold. If the actual bond length in Ag, is 0.1 A longer than reported,I7 R , for AgAu is predicted to be 2.5 8,.
Conclusions The spectroscopic analyses of the calculated potential energy curves show little difference between AREP SCF and REP S C F results. Thus, interatomic spin-orbit coupling effects on the valence electrons in these molecules are negligible for the ground electronic states. In comparing the silver and gold molecular calculations, the magnitudes of the relativistic effects are of reasonable sizes. The contraction in bond length due to relativistic effects is expected to be greater in Au, than in Ag,, and this is the case when the 1 1-electron REP calculations are compared to 11-electron N E P calculations. The contraction in Au, is found to be 0.36 A and that in Ag, is 0.15 8,. The relativistic contraction in Ag, is consistent with that reported by Weltner and Van Zee in their recent review of transition-metal molecules.35
Acknowledgment. This research was partially supported by the National Science Foundation under Grants CHE-8214689 and PRM-8219469. (35) Weltner, W.; Van Zee, R. J. Annu. Rev. Phys. Chem. 1984, 35,291. (36) In this paper the periodic group notation is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., 111 3 and 13.)
-
(34) Huber, K. P.;Herzberg, G. 'Constants of Diatomic Molecules"; Van Nostrand: New York, 1979.
The Chemiluminescent Reaction of N(4S,) Atoms with Azlde Radicals S. J. David and R. D. Coombe* Department of Chemistry, University of Denver, Denver, Colorado 80208 (Received: June 24, 1985)
Discharge-flow methods are used to study chemiluminescence from the reaction of N(4Su)atoms with N3 radicals. The azide radicals are produced by the reaction of HN3 with fluorine atoms. The N + N3 reaction produces intense N2 first positive (B3n, A,&+) emission in the visible and near-IR regions. From the variation of the time profile of this emission with changes in the reagent densities, the rate constant of the F + HN, reaction is determined to be k2 = (1.6 f 0.2) X IO-'o cm3 s-I, and the rate constant of the N + N, reaction is determined to have a lower limit k , 1 6 X lo-" cm3 s-I. For the conditions of these experiments, the yield of B3n, A'&,+ photons relative to the limiting HN3 flow was found to be approximately 20%. The yield of N2(A3Z,+) is such that its presence can be accounted for by radiation from the B3n,state. The high yield of N2(B3n,)can be understood by considering the operation of both spin and orbital angular momentum constraints in the system.
-
-
Introduction A number of experiments performed in recent years have shown that the reactions of gas-phase N, radicals are often strongly constrained to produce electronically excited products by the separate conservation of spin and orbital angular momentum. For example, the reactions of halogen atoms with N 3 produce very high yields of the excited a'A and blZ+ states of the nitrogen halide diatomics.' These reactions are an example of the case where the singlet ground-state potential energy surface of the (,P) + (X2n,)reagents correlates adiabatically to the ground state (X'Z,') of molecular nitrogen and excited singlet states of the (1) A. T. Pritt, Jr., D. Patel, and R. D. Coombe, Int. J . Chem. Kine?., 16, 977 (1984).
0022-3654/85/2089-5206$01.50/0
nitrene. The high yields observed are a result of spin conservation in these systems, which is strong because of the small spin-orbit coupling in the lighter halogens. A significant reduction in the yield of excited singlets is observed in the Br + N3 case relative to F + N 3 or C1 + N3, as expected. Although these systems demonstrate the strength of spin conservation, they offer no information about the role of orbital angular momentum correlations. The 211gground state of N3 correlates to N(,D) + N2(X'Z,+). Hence, to the extent that orbital correlations are important, R + N3 reactions should produce states of the nitrene N R which correlate to R N(,D). For the case of reaction with halogen atoms, both the a'A and b'Z+ excited states of the nitrogen halide diatomics correlate to N(,D), but then these are the only singlet states energetically accessible by the reactions in question. In this paper, we discuss
+
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985
Reaction of N(4S,) Atoms with Azide Radicals
5201
our observations of the reaction of N 3 radicals with nitrogen atoms: N(4S)
+ N3(,IIg)
-*
2N2
(1)
This reaction is exothermic by approximately 215 kcal mol-', sufficient to populate seven different excited electronic statesZof the product N2 molecules. Spin conservation, which should be strong in this light system, would suggest that only triplet or quintet excited states might be produced (assuming the products to be one ground-state and one excited-state N2). To the extent that orbital correlations are important, only those states correlating to N(4S) + N(2D) should be formed. Only two states satisfying both criteria are energetically accessible, the B3n, state and the W3Austate. These states lie in close proximity to one another and are strongly coupled by collision^.^ Angular momentum considerations would therefore suggest the generation of intense A,&+) emission from the N + N 3 N 2 first positive (B311, reaction. Indeed, observation of this emission from N N 3 has been reported by Clark and Clyne4 and by Yamasaki et al.5 The latter authors used a steady-state treatment to extract a rate constant for the reaction, kl = (1.6 f 1.1) X lo-" cm3 s-I. In this report, we describe observations of N + N 3 from experiments in which N3 radicals are produced by the rapid reaction between fluorine atoms and HN3.1 Rate constants for the F H N 3 and N + N 3 reactions are derived from explicit measureA emission. We ments of the time dependence of the N 2 B report measurements of the absolute yield of N 2 B A photons relative to the limiting azide flow and determinations of the N2(A3Zu+)density in the system. These data serve to indicate the remarkable degree to which the N + N 3 system is constrained by both spin and orbital angular momentum correlations. The efficient production of excited triplet metastables of N z is an additional point of interest in this system. N2(A3Z,+) metastables are well-known to participate in energy transfer processes with a variety of atoms and molecules.6 In this regard, considerable recent interest has been focussed on these metastables as a possible energy carrier in chemically pumped laser systems. -+
+
- -
+
Experimental Section The experiments made use of a conventional discharge-flow apparatus. The flow reactor was made from 2.54-cm i.d. Pyrex tubing and had two side arms equipped with 2450-MHz microwave discharges and a concentric slide tube which provided time resolution. The system was pumped by a 650 L min-' mechanical pump, such that the linear velocity of the flowing gases was near 1800 cm s-' for the densities typical of our experiments. The flow rates of the gases were measured with Tylan FM 360 mass flow meters. Fluorine atoms were produced by a discharge through carrier gas/CF4 or carrier gas/F2 mixtures. Nitrogen atoms were generated by passage of carrier gas/N2 mixtures through the second discharge zone. The flow rates of fluorine and nitrogen atoms were determined by chemiluminescent titrations7vswith Cl, and NO, respectively. Azide radicals were provided by the reaction of fluorine atoms with HN3. The HN3entered the reactor through the sliding tube. Emissions from flames produced in the flow reactor were dispersed by a 0.25-m monochromator and detected by a cooled GaAs photomultiplier tube. The P M T response was converted to a voltage signal by an electrometer (Kiethley 610C) and recorded on a strip-chart recorder (Hewlett Packard 7100B). The data were analyzed by using an IBM PC interfaced to a VAX (2) A. Lofthus and P. H. Krupenie, J. Phys. Chem. Ref.Data. 6, 113 (1977). (3) N. Sadeghi and D. W. Setser, J . Chem. Phys., 79,2710 (1983). Also, I. Nadler, A. Rotem, and S. Rosenwaks, Chem. Phys. Lett., 83, 281 (1981). (4) T. C. Clark and M. A. A. Clyne, Trans. Faraday Soc., 66,877 (1970). (5) K. Yamasaki, T. Fueno, and 0. Kajimoto, Chem. Phys. Lett., 94,425 (1983). (6) W. G. Clark and D. W. Setser, J . Phys. Chem., 84, 2225 (1980). (7) P. S. Ganguli and M. Kaufman, Chem. Phys. Lett., 25,221 (1974). (8) See, for example, M. A. A. Clyne in "The Physical Chemistry of Fast Reactions", B. P. Levitt, Ed., Plenum Press: London, 1973, Chapter 4.
WAVELENGTH. nm
-
Figure 1. Spectrum of visible emissions produced by the N + N3reaction. Sequences of the N2 B311g A'&,* transition are identified.
780 computer. Curve fitting and other data manipulations were done with an RS-1 statistical package. Photon yields were measured by calibration of the light collection efficiency of the detection system by using the 0 + N O chemiluminescent reaction as an a ~ t i n o m e t e r . ~For these yield measurements, the monochromator was replaced by a long-pass filter which transmitted wavelengths greater than 510 nm. In this case, a 500-pm wide slit was placed over the reactor window and the detector was moved a distance of 25 cm away from the slit to reduce the overall light intensity impinging on the PMT. H N 3 was generated by the reaction of stearic acid (Mallinckrodt) with NaN, at approximately 363 K. The H N 3 was diluted in helium to produce a 2% mixture and stored in a bulb at room temperature. Argon (99.995%), N z (99.995%), CF4 (99.7%), the N O mixture (1.0% in He), and the C12mixture (3.5% in Nz) were obtained from commercial sources and were not further purified prior to use. During the course of the experiments, however, it became evident that sources of oxygen in the system were to be avoided as much as possible. To this end, gas purifiers (Oxyclear) were installed in the Ar and N 2 lines and the internal surfaces of the flow reactor were coated with halocarbon wax to prevent reaction with the fluorine atoms in the gas stream. Results Spectroscopy of the F / N / H N , Flame. The admission of small flows of HN3 to a stream containing fluorine atoms heavily diluted in argon produced a bright green flame. As was reported previously,'o this emission corresponds to the Av = 0 sequence of the X32- transition in NF. The excited N F is produced by b'Z+ the following series of reactions:
-
F + HN3 F + N3 NF(aIA)
+ N3 NF(alA) + N, NF(b'Z+) + HF*(v-2) HF*(uI5)
-+
+ HF*(v)
(2) (3) (4)
Azide radicals have been positively identified' as a product of reaction 2, and the yield of NF(a'A) from reaction 3 is thought to be near unity. A small flow of nitrogen atoms was admitted to this system, from a microwave discharge through an N2/Ar mixture. The initial density of N atoms, determined by titrations ~, equivalent to the with NO, was typically near lOI3 ~ m - roughly initial F atom density, which was determined by titration' with C1,. The initial HN, density was on the order of 10I2 ~ m - ~ . Admission of the nitrogen atoms to the system produced a very intense orange flame, extending for a few centimeters (Le., a few milliseconds) beyond the mixing zone. The spectrum of this visible (9) A. Fontijn, C. B. Meyer, and H. 1. Schiff, J . Chem. Phys., 40, 64 (1964). (10) R. D. Coombe and A. T. Pritt, Jr., Chem. Phys. Lett., 58,606 (1978).
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985
5208
David and Coombe NO I
0,3
1,5
1,4
x5
,
1.
380
1
3w
370
,
1
3% WAVELENGTH
260
2%
i nm l
-
Figure 4. A portion of the spectrum of ultraviolet emissions produced by the N N, reaction. The spectrum shows bands of the C'II, B'II, (second positive) and A3&+ XiZ,+ (Vegard-Kaplan) systems in N2, and the A%+ X211 (y) and B2n X211 (8) systems in NO.
+
O'OI 0.04
-
0 0
C
- -
-
-7J
- 40 -
N2
Iv -,
Figure 2. Steady-state vibrational distribution in N2(B311,) produced by
the N + N3 reaction. The quantityf(u) represents the fractional population of the level v. The broken line represents an equilibrium thermal distribution characterized by Tvib= 14060 K.
5 35T3
& 30U
25m
-z 20E
I n
151051.0
I
I
2.0
3.0
4.0
I N I T I A L H N 3 DENSlTY(ld2cm3)
Figure 5. Intensity of the second positive emission, measured at the 1,2 band near 354 nm, vs. the initial density of HN,. The solid line represents a quadratic fit to the data.
INITIAL H N ~DENSITY 1 0 ' ~ ~ d )
Figure 3. Intensity of the first positive emission, measured at the 6.3 band near 661 nm, vs. the initial density of HN,. The solid line represents a linear least-squares fit to the data.
emission is shown in Figure 1. All of the features evident in the A3Z,+ transitions in N,. spectrum are attributable to B3n, Features corresponding to the b'Z+ -, X3Z- or aiA -, X3Btransitions in N F (at 528.8 and 874.2 nm, respectively) are absent, suggesting that reactions 3 and 4 above do not occur in the presence of N atoms. The steady-state vibrational distribution among the N2(B311,) molecules in the flame can be calculated from data such as that shown in Figure 1 and the known radiative lifetimes" for the bands of the B A transition. The results of this treatment are shown in Figure 2. The data indicate a substantially relaxed vibrational distribution heavily favoring the lower levels. Some population of levels up to u = 12 (near the dissociation limit of the N 2 ground state) is observed, although a "knee" in the distribution near v = 8 suggests that these higher levels may not be populated directly by the reaction. Indeed, the thermodynamic limit for the N N 3 reaction (AH = -2 15 kcal mol-I) is such that only levels up to v = 8 may be populated directly. It seems likely that the levels above u = 8 arise from scrambling of the nascent population distribution in collisions with the N, and Ar present (densities 2 X l o i 5and 2 X IOi6 ~ m - respectively). ~, Such processes, involving collision-induced coupling with near-resonant levels of the W3A, state, are known to be rapid.3 The strongly relaxed character of the distribution as a whole is a further indication of +
-
+
(1 1)
E. E. Eyler and F. M . Pipkin, J . Chem. Phys., 79, 3654 (1983).
M Jeunehomme, J Chem. Phys., 45, 1805 (1966).
Also
the occurrence of such processes. The relative populations of u = 0 and u = 1 were estimated by extrapolation of an exponential fit (Tvlb= 14060 K) to the data for the levels u = 2 through v = 8 (see Figure 2). A plot of the relative intensity of the B -,A emission, monitored at the 6,3 band near 661 nm, vs. the limiting flow of HN, is shown in Figure 3. The linear variation of the N2 B -,A intensity with H N 3 indicates that the B3n,population arises directly from the N N3 reaction, rather than from second-order processes such as energy pooling12among other excited states of N2. It has been suggested, for example, that N2(B) is produced by energy pooling among N,(A) meta~tab1es.l~ A portion of the spectrum of the flame in the UV region is shown in Figure 4. Features corresponding to the A2Z+ X211 transition (y bands) in NO, the C3n, B3n,(second positive) transition in N2, and the A 3 n X3Z- transition in NH were readily evident. Much weaker features attributable to A38,+ -, X'Z,' (Vegard-Kaplan) bands in N, were observed in the wings of some of the N O bands. The N O bands arise from an oxygen impurity in the flow through the microwave discharges. Separate experiments in our laboratory have shown that the 0 + N3 reaction indeed produces intense N O emission.I4 Gas purifiers (Oxyclear DPG-250) were installed in the argon and N2 source lines in an attempt to alleviate this problem, and in fact a reduction of roughly 75% was observed in the NO intensity. No reduction in the intensity of features identified as Vegard-Kaplan bands was ob-
+
-
-
+
(12) D. H. Stedman and D. W. Setser, J . Chem. Phys., 50, 2256 (1969). ( 13) G. H. Hays and H. J. Oksam, J. Chem. Phys., 59, 1507,6088 (1973). (14) S. J. David and R. D. Coombe, unpublished results.
The Journal of Physical Chemistry, V O ~89, . NO. 24, 1985 5209
Reaction of N(4S,) Atoms with Azide Radicals
-In t z a
m U I
>
t z Lo
K 5
10
0
20
30
40
50
60
TIME ( 1 0 ~ ~ )
Figure 6. Time profile of the first positive emission (6,3 band) for [HN,], = 6.7 X 10” ~ m - [F] ~ , = 3.3 X 10l2~ m - and ~ , [N]= 7.0 X 10” ~ m - ~ . The open circles are the individual data points, and the solid line is a nonlinear least-squares fit to a function Intensity = C(e”I‘ - e-’2‘ ). The first two data points reflect the mixing rate and were not fitted.
served. The remainder of the NO intensity no doubt arises from an O2impurity in the F2 or CF4 sources of fluorine atoms. The NH emission arises from interaction of N,(A) metastables with the HN, reagent. Stedman and Setserls have shown that HN, is dissociated in this process, generating NH(A311). In view of the energy of the N2(C311,)state, it cannot be produced directly by reactions of ground-state reagents present in the flow. Figure B intensity (measured at the 1,2 5 shows a plot of the N2 C band) vs. the HN, flow. As indicated in the figure, the data are closely fit by a quadratic function. This result indicates that N2(C) is produced by a process which is second order in HN3. Since N,(B) [and hence N,(A)] vary linearly with HN,, the origin of the N2(C)is identified as the well-known energy pooling reactionI2 among N2(A) metastables:
-
cm3 s-’. The rate c o n s t a d for reaction 5 is near 2 X Time Behavior of the N2 Emissions. The time profile of the N2first positive emission was measured by movement of the sliding injector (the HN, source) with respect to the fixed observation port. A typical profile, measured for the 6,3 band near 661 nm, is shown in Figure 6. The finite rise time of the emission was unaffected by changes in the flow rates of any of the reagents and hence corresponds to the mixing rate. The decay is well fit by an exponential function. Measurements of the time profile and total intensity of the N, B A emission were made as the concentrations of F atoms and N atoms (both pseudo-first-order reagents) were systematically varied. Concentrations of these species were determined by chemiluminescent titrations with C1, and NO, respectively. The decay time of the first positive emission was found to vary inversely with the fluorine atom density. This behavior is identified as corresponding to changes in the rate of formation of N3by the F HN3 reaction. Figure 7 shows a plot of the decay rate of the N, B A emission vs. the initial density of F atoms. The line shown is a linear leastsquares fit to the data. The slope of the line gives a rate constant k2 = (1.6 f 0.2) X cm3 s-’ for the F HN, reaction. The intercept near the origin indicates that, within the uncertainty of the data shown, this reaction is the only source of N, [and hence N2(B)] in the system. The time profile of the emission was also measured as a function of the N atom concentration. In this case, the complete time profile was fitted to an expression Z ( t ) = C(e-”‘ - d x 2 ’ ) , where A, and X2 are rates for the decay and rise of the emission. Within the uncertainty of the experiment, the values of X1 and X2 were found to be invariant with the N atom flow rate. The time-integrated intensity of the flame increased linearly with the measured N atom density, however, as shown in Figure 8. These data suggest that N atoms compete with another process for removal of N3 from the system. For high N atom densities (>4 X lo1, cm-,), the intensity was invariant with increasing N atom flow, suggesting the dominance of the N + N, reaction in this region.
-
-
+
+
(15) D. H. Stedman and D. W. Setser, Chem. Phys. Lett., 8, 542 (1968).
‘ :!
00
20
IO
40
50
-3
F ATOM DENSITY (10 c m 1
Figure 7. Rate of decay of the first positive emission vs. the density of fluorine atoms. For these data, the initial HN3density was near 6.5 X 10” ~ m - The ~ . solid line is a linear least-squares fit to the data, whose cm3 s-’. slope yields a rate constant k = (1.6 0.2) X
*
-
The time profile of the N2(A)density in the system was determined from the profile of the C 3 n , B3n,emission. Since this emission is produced by reaction 5, its intensity varies as the square of the N,(A) density, such that the N,(A) time profile is given by the square root of the N2C B time profile. The N,(A) profiles determined in this manner exhibited a finite rise time considerably slower than that found for the first positive emission (the mixing rate), followed by a decay which tracked the first positive decay. Hence we identify the decay as the rate of formation of N,(A) [and N,(B)] and the rise as a collisional decay rate. The measured rise times were in fact found to be in good agreement with the measured N atom density and the rate constant reportedlo for N2(A)quenching by these atoms (k = 5 X IO-” cm3 s-I). Yield of N2 B 3 n , A32,+ Photons. Measurements of the total yield of N, first positive photons were made by calibrating the light collection efficiency of our apparatus by comparison with ~ this purpose, chemiluminescence from the 0 NO r e a ~ t i o n .For the monochromator used in most experiments was replaced by a filter which transmitted wavelengths above 510 nm. The PMT cutoff was near 890 nm. To reduce the overall light intensity striking the photocathode of the PMT, a 500-km slit was fixed over the reactor window, and the detector was moved a distance of 25 cm away from the slit. This geometry was used in measurements of intensities from both the NO, and N, systems. Known concentrations of 0 atoms and NO were produced in the reactor by the N + NO titration procedure.* Measurement of the NO2 emission intensity produced by this reaction yields a calibration parameter a,given by -+
-
+
observed intensity (Y=
rkP1 [NO1
where y is the fraction of the total NOz emission detected by the filter/PMT combination, determined from the NO2 emission spectrum and the PMT response. The parameter k is the rate constantg for production of NO2photons by the 0 NO reaction, taken to be 6.3 X lo-’’ cm3 SKI.This two-body rate is appropriate9 to our experiments, which were performed at total pressures near 0.9 torr. The absolute rate of production of N, B A photons from the N/F/HN3 system is then determined from the first positive intensity as follows:
+
-
Jl,bd
photon flow =
dV
Y’a
-
where the observed intensity is integrated over the flame volume, and y’ is the fraction of the B A photons detected by the filter/PMT combination. The value of y’was determined from the PMT response, the vibrational distribution shown in Figure 2 above, and published values2 for the Franck-Condon factors of the transition. The N, B A photon yield is defined as photon flow x 100% @‘e-* = HN3 flow where HN, is the limiting reagent in the system. A number of
5210 The Journal of Physical Chemistry, Vol. 89, No. 24, 1985
David and Coombe
Note that this treatment assumes process 1A to be much faster than process 2, as indeed the data would indicate, and further that the yield of N2(A) from the N N 3 reaction is unity. This would be the case if, for example, the yield of N2(B) were unity and all of the N2(B) decayed radiatively to N2(A). Hence, the expression above gives the maximum density of N2(A) at a time t. The values of k2[HN3I0and k6[Q] are determined by the measured rise and decay rates of the N2(A) time profile. For typical conditions, [A],, is found to be -6 X 10" cm-3 at the point of measurement of the UV spectrum. Hence, the intrinsic yield of N2(A) would appear to be about 15%, in very good agreement with the measured N2 B A photon yield. These data would therefore suggest that all of the N2(A) present in the flame can be accounted for by first positive emission from the N2(B) state.
+
N ATOM DENSITY I IO"cm'1
Figure 8. Intensity of the first positive emission vs. the density of nitrogen atoms. The solid line is a linear least-squares fit to the data.
independent measurements of @ yielded very consistent values in the range 18-22%. Yield of N2(A3Z,+).The density of N,(A) present in the flame can be estimated by assuming that the N 2 C B second positive radiation arises solely from N2(A) energy pooling, reaction 5. This assumption seems quite reasonable in light of the quadratic relation between the second positive intensity and the HN3 flow rate. Under these circumstances, the steady-state density of N2(C) is given by
-
where [A],, is the steady-state density of N2(A) at a particular time (Le., the point at which the second positive intensity is measured), and k,C is the known radiative ratel7 of the C 3 n , B3n, transition, 2.5 X lo7 s-I. Since the density of an emitter is proportional to its emission intensity (in photon flux) divided by the radiative rate, the steady-state density of N2(A) is given by
-
Discussion Based on the data presented above for the F / N / H N 3 system, we propose the following mechanism to account for the behavior of the N2 first positive emission:
-
-
X
lo9 (ZC-B/ZA-.X)
cm-3
where published valuesI8 for krA(the radiative rate of the A3Z,+ XIZg+transition) and k5 [the rate constant for energy pooling producing N2(C)] have been inserted. The krAvalue used, 0.5 S - I , represents an average for the 3Zu+spin components.'* The intensities refer to the total frequency integrated intensities of the C B and A X transitions, in photon flux. Data similar to that shown in Figure 4 indicate an intensity ratio of approximately 40 and hence an N2(A) density of about 1 X 10" cm-), for a measurement near the peak of the N2(A) time profile. Calculations of the intensity ratio made use of published2 FranckX transitions. Also, it Condon factors for the C B and A was assumed that only u = 0 and u = 1 of the A state were populated, as seems reasonable19 given the density of N2 present. The calculated N2(A) density refers to a particular point in the flame. In order to obtain an estimate of the total yield, the finite rates of production and removal of N2fA) must be taken into account. Given the data discussed above, it is reasonable to employ the following model:
-
-
-
F N
+ HN3 + N3
N2(A)
-
+
+Q
+ N3 N2(A) + N2 HF
NAX)
+Q
(2) (1A) (6)
where Q is any quencher of N2(A). The density of N2(A) at a time t is then given by (16) J. A. Meyer, D. W. Setser, and D. H. Stedman, J . Phys. Chem., 74, 2238 (1970). (17) A. W. Johnson and R. G . Fowler, J . Chem. Phys., 53, 65 (1970). (18) D. W. Shemansky and N . P. Carleton, J . Chem. Phys., 51, 682 (1969). (19) D. W. Setser, D. H . Stedman, and J. A. Coxon, J . Chem. Phys. 53, 1004 (1970).
-
-
+
2.5
-
+ HN3 H F + N3 F + N 3 NF(alA) + N 2 N + N 3 N2(B311,) + N2(X1Zg+) M + N 3 products N2(B3n,) N2(A3Z,+) + hv products N2(B311g)+ M F
-+
-
(2) (3) (1)
(7)
(8) (9)
where M refers to unspecified molecules present in flow. Since the rate of removal of N2(B), k8 k9[M], is very rapid with respect to the rate of its formation, a steady-state expression can be used to describe the intensity of the first positive emission:
+
ki [N] [N,] ks + b [ M ] For conditions under which the densities of N and M are much IB-A
=
greater than the density of HN3 (and hence N3), the intensity will track the time dependence of the N 3 density. From the proposed mechanism, the rate equation for N 3 is given by d[N,l/dt = k[F][HN,I
- (k,[F] + ki[N] + b [ M I ) [ N ]
Since the value of k3 has been reportedlo to be 2 X cm3 SKI, process 3 is far too slow to be important for the fluorine atom densities employed in these experiments. Also, since the density of HN, is much smaller than the density of fluorine atoms [HN,] = [HN3]oe-k2[F]' The time dependence of the N 3 density is therefore given by
-
From the experiments, the term e-'Q[qtcorresponds to the decay of the B A emission, and we find k2 = 1.6 X cm3 s-I. Since the observed rise of the emission did not vary with [N], the term kl[N] + k7[M] must exceed the finite mixing rate in the system. Further, k7[M] must be a significant contributor to the removal of N 3 at low N atom densities, since under these conditions the intensity at a given time increased linearly with [N] or [HN,], for a fixed flow of F atoms. For N atom densities greater than -4 X lOI3~ m - reaction ~, 1 would appear to dominant N 3 removal as indicated by the independence of the first positive intensity on [N] and the high photon yields found in this regime. In this case, the rise time sets a lower limit on the rate constant for reaction 1. This treatment yields a value k l 1 6 X IO-" cm3 s-l. The rate constant reported by Yamasaki et al.,5 (1.6 i 1.1) X lo-" cm3 s-I, was obtained from a steady-state treatment of the N/Cl/HN3
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985 5211
Reaction of N(4S,) Atoms with Azide Radicals reaction. These authors assumed a mechanism in which N and C1 atoms compete for N3 produced by C1 + HN,, a relatively slow process with a rate constantZoof 1 X cm3 s-I. Since in the present experiments the F N3 reaction is completely negligible, the operation of a reaction such as process 7 is required in order to explain the increase in intensity with N atoms for [N] 5 4 X 1013~ m - ~In. principle, reaction 7 should also be important in the N / C I / H N 3 system, since in the experiments by Yamasaki and co-workers the sum of the N and C1 atom densities was . of reaction 7 in apparently on the order of l O I 3 ~ m - ~Inclusion the mechanism of the N/C1/HN3 system would result in calculation of a larger value of k , from the steady-state treatment. Hence, our data tend to support the higher value noted above. The exact nature of reaction 7 is unknown. Its operation has been suggested by a number of previous experiments with azide systems, however. In the reactions of F atoms or mixed F and C1 atoms with HN,, the admission of SF6or COz to the reaction medium was observed to nearly double the intensities of emissions from excited singlet states of N F or NCI, respective1y.l One interpretation of this phenomenon is that these molecules serve to stabilize N 3 radicals produced by F + HN3. This picture is supported by measurements2' of the vibrational distribution in the NF product of this reaction, which is nearly statistical and heavily favors lower u levels. It seems likely, therefore, that a sizable proportion of the 5 5 kcal mol-' released by F HN3 appears as internal excitation in N,. Hence, loss of N3 from the system may occur by unimolecular dissociation or by dissociation in collisions with species M (reaction 7). Since insufficient energy is available to produce the adiabatic dissociation products N(2D) N2(X1Zg+),collisions may be required to stimulate a jump to the quartet potential energy surface leading to N(4S) + N2(X). Thermodynamically, dissociation to these ground-state fragments may require as little as 12 kcal mol-'. The true barrier height, defined by the position of the doublet-quartet curve crossing, is likely to be considerably higher, however. The measured N 2 B A photon yields simply represent the flow of first positive photons relative to the HN, flow, for the particular conditions of our experiments. In all probability the actual branching fraction for production of N2(B) by N N, is much greater than the photon yield, since collisional quenching of N2(B) or removal of N3 by other paths has not been taken into account. As noted above, addition of large flows of C 0 2 or SF6 were found to nearly double the photon yields from halogen atom reactions with N3, presumably by stabilization of the fragile azide radicals.' No such additives were employed in the present experiments, primarily because of the susceptibility of N2(B311,) to collisional quenching. This state is strongly coupled by collisions to the nearby W3A, state, such that the equilibrium-weighted lifetimes of coupled pairs of states can be considerably longer (by as much as an order of magnitude) than the lifetime of the B3n, state in the absence of collision^.^ These extended lifetimes are such that collisional quenching can be a significant problem at the densities of our experiments. For example, admission of COz to the system at a density of 2 X lOI4 cm-, (about a factor of 30 smaller than the densities employed in the halogen atom-N3 experiments) was found to quench the visible first positive emission to one-half its initial value. It would seem, therefore, that optimum operation of the N + N, reaction may well involve a trade-off between stabilization of the N3 radicals and quenching of excited N2. The high yield of N2(B) can be understood by considering the angular momentum constraints operative in this system. Conservation of spin angular momentum would suggest that N(4S) + N3(%,) could produce one ground-state N2 molecule and one excited N 2 molecule in either triplet or quintet states. Since there are several excited triplet states energetically accessible by this reaction, spin conservation cannot explain the specificity with
N+N,
400
+
300
200
\
IO0
+
+
-
+
(20) A. T.Pritt, Jr., and R. D. Coombe, Int. J . Chem. Kinef., 12, 741 (1980). (21) J. J. Sloan, D. G.Watson, and J. S . Wright, Chem. Phys., 43, 1 (1979).
0 Figure 9. Partial correlation diagram for the N
+ N3
-
2N2 reaction.
which N2(B) is produced. If only spin were important, one would expect preferential population of the lowest energy triplet [N2(A)], contrary to the experimental results. Hence, we conclude that orbital angular momentum must also play an important role. Considering the system in a simple way, we expect N, to behave chemically like an N(2D) atom weakly bound to ground-state Nz(XIZg+),such that reaction with ground-state N atoms should produce excited states of N 2 correlating to N(2D) N(4S), Le., the B3n, or W3A, states. These ideas can be expressed by consideration of possible orbital correlations in the manner originally described by Shuler.22 Figure 9 shows a partial correlation diagram for the N N3 system, assuming that the intermediate N4 configuration is of C, symmetry (as are the molecular azides RN,) and that spin-orbit coupling is small. As shown in the figure, the reactants N(4S) + N3(211s)correlate adiabatically only to products N2(B311,) + N2(X'Zg+)or N2(W3Au)+ N2(X'Z,+) by a potential energy surface of species 3A' ,A''. The ground-state products N2(X'Zg+) + N2(X'Z,+) correlate via a 'A' surface to [N(4S) N3(42-)]. This excited state of N3 is repulsive and dissociates to N(4S) N2(X'Zg+). These same reagents [N(4S) N3(4Z-)]correlate via a ,A' surface to N2(A3Z1+) N2(X'2,+), and via a 5A' surface to the proposed sZcq+ state of N 2 and N2(X'Z,'). The surface of species ,A'' arising from N(4S) N3N2(X1Z,+). The 2Zu+ (zZ+,) is likely to correlate to N,(B'%;) state of N3 (the upper state of the well-known transition near 270 nmz3)and N2(B') are both thought to dissociate to N(*P). Several singlet and triplet surfaces of species A' A" arise from the reagents N(2D) N3(211g).These surfaces may lead to a number of excited N2 products, including a%,, a'lZ;, W'A,,, bin,, H3@,, and b'lZ,', all of which are thought to dissociate to N(2D) + N(2D).2 Hence, it is apparent that the reaction Of N3(,IIg) radicals with ground-state N atoms is constrained to produce only the B3n, or W3& states of the excited N2product, whereas a much broader array of excited states may be produced by reaction with N(2D) atoms. The present data offer a further demonstration of the utility of the F + H N 3 reaction as a source of gas-phase N 3 radicals.
+
+
+
+
+
+
+
+
+
+
+
~
~~~~~
(22) K.E.Shuler,J . Chem. Phys., 21, 624 (1953). (23) A. E. Douglas and W. E Jones, Con. J . Phys., 43, 2216 (1965)
5212
J . Phys. Chem. 1985, 89, 5212-5217
The rate constant for this reaction, 1.6 X cm3 s-’, is nearly two orders of magnitude greater than that for reaction of the product N, radicals with fluorine atoms. Hence, N, can be made very rapidly for consumption by an added reagent, such as N(4S) atoms in the present case.
Acknowledgment. This work was supported by the US.Air Force Weapons Laboratory, Contract No. F29601-84-C-0094. The authors are grateful to Professor D. H. Stedman of the University of Denver for helpful discussions during the course of the work.
Diffusion-Controlled Reactions of Isotropic Reagents and Molecules wlth Two Active Sites. Effect of Competition of the Active Sites for the Reagent I. A. Pritchin and K. M. Salikhov* Institute of Chemical Kinetics and Combustion, Novosibirsk 630090, USSR (Received: July 23, 1984)
Bimolecular reaction rate constants have been calculated for spheric reagents: isotropic particles and bifunctional molecules. Effective steric factors have been determined for various radii of reagents and various sizes of active sites. The effect of competition of active sites for reagents has been analyzed. The results of numerical calculations have been summarized as plots which can be used for determining the effective steric factors and the active site sizes with the help of experimental data on reaction rate constants for mono- and bifunctional molecules.
Introduction A bimolecular reaction in liquids is featured by the stage of forming a “pair” from the reagents that encounter inside a certain “cage”.1.2 The encountering reagents reside in the “cage” for some time. For uncharged particles this time is within a nanosecond range; for charged ones it can reach thousands of nanoseconds. During these times the reagents inside the cage are liable to reencounters. In time intervals between the reencounters there occur various processes affecting the reaction product generation. The cage effect manifests itself in quite a number of ways. Most prominently it shows up as chemically induced nuclear polarizations and magnetic effects in radical reactions (see, e.g., ref 3-5). Also the cage effect in liquid-phase reactions appears as averaging the anisotropic reactivity of particles by their translational and rotational d i f f ~ s i o n s . ~ - I ~ An interesting cage effect arises in reactions involving particles with several active groups. Such particles can reencounter through different groups. As a result the reaction of one active group depends on whether or not this very reagent has other active groups; Le., the contribution from the reacting groups to the total (1) Franck, J.; Rabinowitch, E. Trans. Faraday Soc. 1934, 30, 120. (2) Noyes, R. M. ’’Progress in Reaction Kinetics”; Pergamon: New York, 1961; Vol. 1, Chapter 5. (3) Bargon, J.; Fischer, H.; Johnsen, U. Z . Nuturfarsch., A 1967, 22A, 1551. (4) Kaptein, R.; Oosterhoff, J. L. Chem. Phys. Lett. 1969, 4, 195. (5) Molin, Yu. N.: Sagdeev, R. 2.; Salikhov, K. M. Rev.Sou. Authors, Chem. Ser. 1979, I , 1 . (6) Solc, K.; Stockmayer, W. H. J . Chem. Phys. 1971,54, 2981. ( 7 ) Solc, K.; Stockmayer, W. H. Int. J . Chem. Kinet. 1973, 5, 733. (8) Doi, M. Chem. Phys. 1975, 11, 115. (9) Salikhov, K. M. Tear. Eksp. Khim. 1977, 13, 732. (10) Samson, R.; Deutch, J. M. J. Chem. Phys. 1978, 68, 285. (11) Zientara, G. P.; Freed, J. M. J . Phys. Chem. 1979, 83, 3333. (12) Levin, P. P., Burlatsky, S. F.; Ovchinnikov, A. A. Teor. Eksp. Khim. 1980, 16, 746. (13) Berdnikov, V. M.; Doktorov, A. B. Tear. Eksp. Khim. 1981, 17, 318. (14) Doktorov, A. B.; Lukzen, N. N. Chem. Phys. Lert. 1981, 79, 498. (IS) Doktorov, A. B.; Yakobson, B. I. Chem. Phys. 1981,60, 223. (16) Shoup, D.; Lipari, G.; Szabo, A. Biophys. J . 1981, 36, 697. (17) Temkin, S. I.; Yakobson, B. I. J. Phys. Chem. 1984, 88, 2679. (18) Temkin, S. I.; Yakobson, B. I. Khim. Fiz. 1984, 3, 1658. (19) Huddleston, R. K.; Mulac, W. A. J . Phys. Chem. 1982, 86, 2279.
rate constant becomes nonadditive: the active groups compete for the reagent. That competition has been found out experimentally in studying the reactions of solvated electrons with molecules involving two functional acceptor groups.19 The measured reaction rate constant KI2for bifunctional molecules has been comparedI9 with the constants K 1 and K2 for analogous monofunctional molecules ( K , # K2 if the acceptor groups are different). The nonadditive contribution from two acceptor groups in one molecule is characterized by the parameter If the functional groups of the same molecules did not compete, we should have 4 = 1. For a number of bifunctional molecules reacting with solvated electrons 4 < 119 which proves the nonadditive contribution from active groups to the reaction rate constant, In the present paper the effect of competition of two active sites for a reagent has been analyzed theoretically. It has been shown that comparative studies on reactions of mono- and bifunctional molecules allow independently effective steric factors.
The Model: Calculation Technique Assume the reacting particles A and B to be spheres with radii RA and Rg. Let the B particles have isotropic reactivity and move with a diffusion coefficient Dg. For example, solvated electrons may be such parti~1es.I~ An A particle reacts only by a portion of its surface, namely, by two axially symmetric active sites with an angular size 0, (Figure 1). The A particles move translationally with a diffusion coefficient DA and rotate with a rotational diffusion coefficient DR. The relative location of the reagents is set by the distance r between their centers and the polar angle B between the direction r and the axis of symmetry for A molecules. Taking into account translational and rotational particle diffusions, the stationary density distribution C(r,0) for B particles relative to a particular A molecule is6
ec = 0 1 = DV2 + DR sin-’ 0
0022-3654185 12089-5212%01.50/0 , 0 1985 American Chemical Society I
,
ae
where D = DA + Dg is the coefficient of relative diffusion of A and B particles.
